Depending on if you live in a city, you may want to check local ordinances about enclosures. I know my city stipulates that runs/enclosures "must be impermeable to rodents, wild birds and predators, including dogs and cats," and that "windows and vents [on coops] must be covered with predator and bird proof wire of less than one (1) inch openings."
If you're not in a city, it's probably up to your best judgment!
"georgiagail - Do your gates in the run allow you access to it or did you cover over them with hardware cloth? Do you ever have problems with anything (chicken or otherwise) squeezing through the gaps in the gate?"
We also cover the gate with hardware cloth and then extend the cloth to the end of the fence, allowing for a bit of "looseness" to be able to swing the gate open. Nothing has squeezed through the gaps in the gate (yet).
My runs are poultry wire and I lock my chickens in at night. My hoop coop is hardware cloth and I lock the door at night which is inside the run. I "mark" my yard every chance I get and thank the good Lord things are good.